You should be able to feel the ribcage when you run your hands back and forth along the body. Looking down along the dog's back, they should be slightly smaller just under the ribcage, this is their waist. The hipbones at the back should not be prominent in any way. If you can see the ribcage, your dog is underweight. From what you say, I doubt that is the case. Addie was also small at a bit over 5 months. She gained weight slowly.
I might be overstepping my bounds here, but when I read your post, my first reaction was, get a new vet. He's doubling the number of vaccines on a dog he considers underweight?
As for food, if you are interested in changing, dogfoodanalysis.com has ratings for dog food, plus you can find many opinions on the topic of food on this forum.
Treats should be fine, just read labels. All natural ingredients, stay away from artificial preservatives like BHA and BHT (this goes for dog food, too).